# Seeing fundamental groups through intersection theory

# Seeing fundamental groups through intersection theory

Start:

Monday, November 4, 2024 12:00 pm

End:

Monday, November 4, 2024 12:50 pm

Location:

111 STAG

Dev Sinha

University of Oregon

In a manifold, one can define first cohomology classes by intersection with codimension one submanifolds by counting intersections. For example, winding number around the origin can be defined through intersection with the positive x-axis. If one has multiple such submanifolds, one can also track the order in which such intersections occur. For example, one can show Borromean rings are linked by tracking intersections of one component with Seifert surfaces of the others in this way. I will share recent and current work which formalizes and applies this idea, giving for example very concrete ways to determine if a word in a finitely presented group is a multiple of a k-fold commutator.

Contact:

Chad Giusti